3.642   ODE No. 642

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{{(-{\left(y\left(x\right)\right)}^2+4ax)}^2}{y\left(x\right)}=0}}$$

1. Problem in Latex
2. Mathematica input
3. Maple input

Mathematica: cpu = 0.145018 (sec), leaf count = 105 $$\{\{y(x)\to -\sqrt{4ax-\sqrt{2}\sqrt{a}\tanh \left(\frac{2\sqrt{2}ax-\sqrt{2}{c}_1}{\sqrt{a}}\right)}\},\{y(x)\to \sqrt{4ax-\sqrt{2}\sqrt{a}\tanh \left(\frac{2\sqrt{2}ax-\sqrt{2}{c}_1}{\sqrt{a}}\right)}\}\}$$

Maple: cpu = 0.187 (sec), leaf count = 286 $$\{y\left(x\right)=\sqrt{4}\sqrt{(\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{2x(\sqrt{2}\sqrt{a}-2ax)}+{\mathrm{e}}^{-2x(\sqrt{2}\sqrt{a}+2ax)})(\mathit{\_}\mathit{C}\mathit{1}(ax-\frac{\sqrt{2}}{4}\sqrt{a}){\mathrm{e}}^{2x(\sqrt{2}\sqrt{a}-2ax)}+{\mathrm{e}}^{-2x(\sqrt{2}\sqrt{a}+2ax)}(ax+\frac{\sqrt{2}}{4}\sqrt{a}))}{(\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{2x(\sqrt{2}\sqrt{a}-2ax)}+{\mathrm{e}}^{-2x(\sqrt{2}\sqrt{a}+2ax)})}^{-1},y\left(x\right)=-\sqrt{4}\sqrt{(\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{2x(\sqrt{2}\sqrt{a}-2ax)}+{\mathrm{e}}^{-2x(\sqrt{2}\sqrt{a}+2ax)})(\mathit{\_}\mathit{C}\mathit{1}(ax-\frac{\sqrt{2}}{4}\sqrt{a}){\mathrm{e}}^{2x(\sqrt{2}\sqrt{a}-2ax)}+{\mathrm{e}}^{-2x(\sqrt{2}\sqrt{a}+2ax)}(ax+\frac{\sqrt{2}}{4}\sqrt{a}))}{(\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{2x(\sqrt{2}\sqrt{a}-2ax)}+{\mathrm{e}}^{-2x(\sqrt{2}\sqrt{a}+2ax)})}^{-1}\}$$